This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles. Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation theorem frequently plays a key role. Slutsky´s idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopf theorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes. Although these two targets are the principal ones, a large number of results from Fourier analysis must be prepared in order to reach these goals. The basic concepts and results from classical as well as generalized Fourier analysis are provided in a systematic way. Prospective readers are assumed to have sufficient knowledge of real, complex analysis. However, necessary economic concepts are explained in the text, making this book accessible even to readers without a background in economics.
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
This book presents a wealth of images of shock wave phenomena, gathered by the author over the past 40 years. Shadowgrams and interferograms of basic shock-dynamic topics such as reflection, diffraction, refraction, and focusing of shock waves in gases and liquids are sequentially displayed. Though the images themselves are self-explanatory, brief explanations of the experimental conditions are included, so as to facilitate analysis and numerical reproduction of the image data. In addition, the book presents interferometric observations of underwater shock wave/bubble interactions, and highlights the multifaceted applications of shock wave phenomena to medicine and industry. Given its scope, the book offers a unique resource for students and researchers who are interested in shock wave phenomena. However, the content has also been specifically prepared for the benefit of readers who are interested in gas dynamics and medical applications of shock waves, and are looking for reliable experimental images.
This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15-19 August, 2016. This volume contains ten research articles authored by several of Varadhan´s former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan´s deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.
A team of sociologists presents a groundbreaking model of concepts and categorization that can guide sociological and cultural analysis of a wide variety of social situations. Using this model, important yet commonplace phenomena such as routine buying decisions can be quantified in terms of the cognitive distance between concepts.
This volume aims to stimulate discussions on research involving the use of data and digital images as an understanding approach for analysis and visualization of phenomena and experiments. The emphasis is put not only on graphically representing data as a way of increasing its visual analysis, but also on the imaging systems which contribute greatly to the comprehension of real cases. Scientific Visualization and Imaging Systems encompass multidisciplinary areas, with applications in many knowledge fields such as Engineering, Medicine, Material Science, Physics, Geology, Geographic Information Systems, among others. This book is a selection of 13 revised and extended research papers presented in the International Conference on Advanced Computational Engineering and Experimenting -ACE-X conferences 2010 (Paris), 2011 (Algarve), 2012 (Istanbul) and 2013 (Madrid). The examples were particularly chosen from materials research, medical applications, general concepts applied in simulations and image analysis and other interesting related problems.
So behalten Sie Nerven und Kurse im Griff. This is an in-depth and comprehensive analysis of the complex thermodynamic and dynamic phenomena experienced by a diesel engine during load increase, acceleration, cold starting or Transient Cycle, presenting the most important findings in the field. Psychologie spielt im Börsengeschehen bekanntermaßen eine große Rolle. Sie bietet nachvollziebare Erklärungen und wichtige Hinweise zum Verständnis von Kursschwankungen, die durch wiederkehrende Verhaltensmuster ausgelöst werden. Insbesondere Massenphänomene lassen sich an der Börse immer wieder beobachten. Wer sie durchschaut, ist im Vorteil und kann sein Anlage- und Beratungsverhalten optimieren. Masseneuphorien und Panikreaktionen bestimmen Kursverläufe. Die Gefühlsreaktionen der Anleger werden ständig durch psychologische Gestzmäßigkeiten beeinflusst, die sich in beeindruckender Regelmäßigkeit wiederholen. Dieses Buch erklärt die Zusammenhänge und bietet auf dieser Basis eine Vielzahl von Anregungen und Hilfestellungen für Berater und Anleger.